The lawmakers made the call on Tuesday while adopting a motion brought under matters of urgent national importance by Olajide Olatunbosun.
The motion focussed on the 774,000 temporary jobs to be created in public works, initiated by the Buhari administration.
The jobs led to a disagreement between the lawmakers and the minister of state for labour, Festus Keyamo.
Mr Argungu is believed to have sided with the lawmakers.
The lawmakers condemned the sack of the DG whom they described as a man that stood up for the right thing to be done.
President Muhammadu Buhari had last week, through his spokesperson, announced Mr Argungu’s sack.
No reason was given for the sack and the directive was meant to take effect from Monday, December 7.
Mr Keyamo was directed to nominate an Acting DG from amongst the most senior directors based on competencies and seniority to take over from Mr Argungu until a substantive holder of the post is appointed by the president.
The Senate had also urged the president to reconsider and rescind his decision on the sack of the DG.
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